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Paper   IPM / M / 17460
School of Mathematics
  Title:   Local models for the moduli stacks of global $\mathfrak{G}$-shtukas
  Author(s):  Somayeh Habibi (Joint with E. Arasteh Rad)
  Status:   Published
  Journal: Math. Research Letters
  Vol.:  26
  Year:  2019
  Pages:   323-364
  Supported by:  IPM
In this article we develop the theory of local models for the moduli stacks of global G-shtukas, the function field analogs for Shimura varieties. Here G is a smooth affine group scheme over a smooth projective curve. As the first approach, we relate the local ge- ometry of these moduli stacks to the geometry of Schubert va- rieties inside global affine Grassmannian, only by means of global methods. Alternatively, our second approach uses the relation be- tween the deformation theory of global G-shtukas and associated local P-shtukas at certain characteristic places. Regarding the anal- ogy between function fields and number fields, the first (resp. sec- ond) approach corresponds to Beilinson-Drinfeld-Gaitsgory (resp. Rapoport-Zink) type local model for (PEL-)Shimura varieties. This discussion will establish a conceptual relation between the above approaches. Furthermore, as applications of this theory, we discuss the flatness of these moduli stacks over their reflex rings, we intro- duce the Kottwitz-Rapoport stratification on them, and we study the intersection cohomology of the special fiber.

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